Faculty of Physics
M.V.Lomonosov Moscow State University
Theoretical and mathematical physics

## A static spherical-symmetric model in the scalar-tensor theory of gravitation

### V.I. Denisov, J.J. Hernandez

Moscow University Physics Bulletin 1999. 54. N 2. P. 1

A system of nonlinear differential equations in a new-type scalar-tensor gravitation theory in the case of a static spherical-symmetric source has been integrated. A post-Newtonian expansion of the solution has been developed. The theory predictions have been shown to agree with the results of all the experiments carried out in the Solar System's weak gravitational field. The essential difference between the metric obtained and the Schwarzschild metric in the strong field region has been demonstrated.

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## Nonlinear vacuum effects and optical properties of nonconducting crystals in intense electromagnetic fields

### V.N. Rodionov

Moscow University Physics Bulletin 1999. 54. N 2. P. 5

Based on the exact solutions of quantum equations of charged particles motion in the combination of a constant magnetic field and a wave field, the cross sections and probabilities of $e^{+}e^{-}$ photo-production and nuclear $\beta$-decay processes have been calculated. It has been demonstrated that the expressions obtained with account for the field action on the normalized characteristics of the process $\gamma^{'} +\gamma^{''} \to e^{+} + e^{-}$ can also be applied to characterize the absorption coefficients of nonconducting crystals in the field. A field-dependent instability of a proton in an intense external field has been estimated. It has been observed that conditions may arise for an effective $\beta$-transformation of nucleons at a heavy nuclei boundary.

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## Dependence of particular solutions of one-dimensional nonlinear Schr$\stackrel{..}{o}$dinger-type equations on problem parameters

### A.R. Frenkin

Moscow University Physics Bulletin 1999. 54. N 2. P. 11

The dependence of particular solutions of generalized one-dimensional Schr$\stackrel{..}{o}$dinger-type equations on problem parameters has been studied. The relationship between weak and strong separatrix solutions has been established. The equations with different-type nonlinearities have been considered.

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## Upper and lower variational estimates in calculating the three-particle systems with exponential trial functions

### A.G. Donchev, N.N. Kolesnikov, V.1. Tarasov

Moscow University Physics Bulletin 1999. 54. N 2. P. 16

All the formulas necessary for calculating not only the upper $E_U$, but also the lower $E_L$ variational estimates of three-particle system energy with the use of trial functions in the form of expansions in multi-dimensional exponents are obtained. The lower variational estimates with such trial functions are found for the first time. It is shown on some examples that, though $E_L$ is usually a more distant estimate of the system energy exact value $E_0$ than $E_U$, it provides also an appreciably more reliable extrapolation.

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Atomic and nuclear physics

## Calculations of electron loss cross sections for oxygen ions in gaseous media

### I.S. Dmitriev

Moscow University Physics Bulletin 1999. 54. N 2. P. 23

In the ion energy range 0.1-200 MeV/nucleon, the cross sections $\sigma_{i, i+1}$ of electron loss by oxygen ions with charges $i=1 \div 7$ in hydrogen, nitrogen, and argon are calculated. The values of the cross sections of electron loss by multielectron ions are obtained by summing up partial cross sections $\sigma_{nl}$ of electron losses from all $nl$ ion shells. The charge composition in the oxygen ion beams after passing the specified substance layer is determined. Most calculation results are fairly consistent with the experimental data available.

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## Detection of incoherent trains of "gravity" pulses with unknown noise distrubution

### A.V. Gusev, V.N. Rudenko

Moscow University Physics Bulletin 1999. 54. N 2. P. 29

The problem of threshold level selection is discussed in a detector of incoherent train of "gravity" pulses under unknown noise distribution without using any hypothesis on the form of that distribution.

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Optics and spectroscopy

## Nonlinear collisional relaxation of two-level atoms in laser field

### B.A. Grishanin

Moscow University Physics Bulletin 1999. 54. N 2. P. 35

Based on the quantum analog of the Boltzmann equation, the task of calculating the excitations of two-level atoms in the gaseous phase, taking into account their resonance dipole-dipole collisional broadening, is considered. The dependence of relaxation matrix parameters on laser field parameters induced by the field dependence of the state of colliding active atoms is analyzed.

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Acoustics and molecular physics

## Polarization effects in transverse acoustic wave reflection by nonlinear boundary

### F.M. Severin, I.Yu. Solodov, B.A. Korshak

Moscow University Physics Bulletin 1999. 54. N 2. P. 41

The polarization of second-harmonic acoustic waves is theoretically studied for the case of nonlinear reflection of a linearly polarized transverse wave by a free solid boundary. Angular dependences of the generation efficiencies for different types of second-harmonic waves are calculated. It is shown that in the subcritical region, the second-harmonic waves are linearly polarized, the polarization of the reflected transverse harmonic being different from that of the primary reflected wave. In the supercritical region, the transverse second-harmonic wave becomes elliptically polarized. The basic theoretical conclusions are confirmed by experimental data.

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Solid state physics

## Temperature behavior features of Ni1oo-xP x alloys magnetization in the region of magnetic phase transition

### S.D. Antipov$^1$, G.E. Goryunov$^1$, M.V. Ivanov$^2$, A.L. Kolumbaev$^1$, Yu.M. Polukarov$^2$, P.N. Stetsenko$^1$, Zhang Yiangao$^1$

Moscow University Physics Bulletin 1999. 54. N 2. P. 46

The Ni$_{100-x}$P$_x$ alloy films ($x=2,44\div16,8$ ат.% Р) were synthesized by chemical deposition on copper substrates. X-ray diffraction and magnetic measurements showed that, initially, the alloy was in a nanocrystalline superparamagnetic state. Temperature studies of magnetization for the alloy with $x=16,8$ ат.% Р revealed the occurrence of anomalous heat release and heat absorption in the magnetic phase transition region.

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## Energy spectrum of radiation defects in Pb$_{1-x}$Sn$_x$Se ($x\le0,\!06$) alloys irradiated by electrons

### N.B. Brandt, E.P. Skipetrov, B.B. Kovalev, L.A. Skipetrova

Moscow University Physics Bulletin 1999. 54. N 2. P. 52

At pressures $P\le18$ khar, galvanomagnetic effects in $n$- and $p$-Pb$_{1-x}$Sn$_x$Se ($x\le0,\!06$) alloys irradiated by electrons were studied. The metal-dielectric and dielectric-metal transitions induced by electron irradiation and hydrostatic compression of irradiated crystals were observed. These transitions were attributed to the appearance of a deep radiation defect level $E_{t1}$ near the $L_6^+$ valence hand top. An energy diagram of the pressure-induced level shifts with respect to allowed energy band edges at point $L$ of the Brillouin zone was constructed.

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## M$\stackrel{..}{o}$ssbauer study of $^{57}$Fe and $^{119}$Sn nuclei hyperfine coupling in the $\beta$-Mn$_{18}$Sn$_{2-x}$Fe$_x$ system

### V.S. Rusakov$^1$, A.S. Ilyushin$^1$, A.S. Vinogradova$^1$, I.A. Nikanorova$^1$, V.M. Cherepanov$^2$

Moscow University Physics Bulletin 1999. 54. N 2. P. 59

By measuring their $^{57}$Fe and $^{119}$Sn MOssbauer spectra, the Mn$_{18}$Sn$_{2-x}$Fe$_x$ alloys ($x=0,\!0\div2,\!0$) with the $\beta$-Mn structure were studied. The hyperfine coupling parameters of $^{57}$Fe and $^{119}$Sn nuclei in various nonequivalent lattice sites, depending on the radius of the first coordination sphere, were analyzed. The mechanisms determining the hyperfine electric interactions of $^{57}$Fe and $^{119}$Sn nuclei were considered. The predominantly covalent character of the electronic structure of $\beta$-Mn-Sn-Fe alloys was shown.

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Geophysics

## Electric fields of celestial bodies

### V.I. Grigor'ev, E.V. Grigor'eva

Moscow University Physics Bulletin 1999. 54. N 2. P. 65

Numerical estimates for the electric fields strengths induced by tidal forces on the surfaces of some planets and their satellites are obtained.

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## Currents generated by water solitons

### S.A. Arsen'ev, O.A. Zhivogina, N.K. Shelkovnikov

Moscow University Physics Bulletin 1999. 54. N 2. P. 68

Currents have been theoretically simulated in the field of solitary water waves. The calculation formulas found correspond to the data of laboratory experiments.

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Astronomy

## Rotation of solid Earth core in the field of nonequilibrium Earth shell

### S.L. Pasynok

Moscow University Physics Bulletin 1999. 54. N 2. P. 74

The influence of nonequilibrium Earth shell on the rotation parameters of the Earth's inner core is studied. An expression for a part of the mutual force function of an elliptic solid core and a nonequilibrium shell is developed. The expression contains the Euler angles. The solid core rotation parameters for the case when no liquid core exists are calculated. It is shown that the effect resulting from the existence of a nonequilihrium shell must he taken into account in rotation theories that are linear with respect to compression. For this purpose, the force function calculated in the present study can he used.

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Theoretical and mathematical physics

## One-loop energy corrections in the non-Abelian gauge field theory in 2+1 dimensional space-time

### V.Ch. Zhukovskii, N.A. Peskov

Moscow University Physics Bulletin 1999. 54. N 2. P. 79

Exact constant solutions for the Yang-Mills fields in the classical non-Abelian field theory with the Chern-Simons topological mass term in the 2+1 dimensional space-time are obtained. One-loop contributions of the boson and fermion fluctuations to the gauge field energy are calculated.

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## Measurement reduction in a fuzzy experimental model as a solution of nonlinear programming problems

### K.V. Kirillov, A.I. Chulichkov

Moscow University Physics Bulletin 1999. 54. N 2. P. 83

Problems of estimating the object parameters under fuzzy restrictions imposed on the coordinates of noise vectors and input signal in the specified orthonormal bases of relevant spaces are solved.

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## The expanding compacta method for solving ill-posed problems under sourcewise representability condition

### A.G. Yagola, K.Yu. Dorofeev

Moscow University Physics Bulletin 1999. 54. N 2. P. 87

It is shown that the condition of sourcewise representability of the exact solution to an operator equation of the first kind widely applied in theoretical studies allows one not only to construct a method which is optimal with respect to the accuracy order, but also to produce an a posteriori error estimate. The method of expanding compacta is proposed.

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Geophysics

## Effect of suspensions on variations of heat and mass exchange between ocean and atmosphere

### Yu.G. Smirnova, E.V. Karavaeva, G.G. Khundzhua

Moscow University Physics Bulletin 1999. 54. N 2. P. 91

Laboratory studies show that the heat fluxes from the surface strongly depend on the presence of suspensions in the water.

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